Citing divisions within the Quartet, Hamad said: "I believe there is a possibility to change the Quartet's position in a more positive manner to deal with the government."
The Quartet, comprising the United States, the European Union, Russia and the United Nations, repeated a demand on Wednesday that any Palestinian government renounce violence, recognise Israel and respect interim peace deals.
But the unity government deal between the ruling Hamas movement and the Fatah faction of Mahmoud Abbas, the Palestinian president, widened divisions within the Quartet.
The United States wants to continue to shun the government if it does not meet the three conditions, whereas Russia and other European governments favour a softer line.
Ismail Haniya, the Hamas-appointed prime minister, has said he hopes to announce a new government within three weeks.
Ahmed Abdel-Rahman, an Abbas adviser, said the Quartet "will open the door" to restoring ties with the Palestinian government once it fully understands the unity government deal.
Russia has been reticent about maintaining an aid embargo imposed by Western governments after Hamas won elections last year and has urged a softening of the Quartet's stance.
The EU, like Russia, appears to favour a softer line, seeing the new Palestinian unity government as a solution to factional violence, although the EU has not pushed for a resumption of aid to the Palestinians.